/// <summary>Returns a sub matrix extracted from the current matrix.</summary>
/// <param name="r">Array of row indices</param>
/// <param name="j0">Start column index</param>
/// <param name="j1">End column index</param>
public MatrixV Submatrix(int[] r, int j0, int j1)
{
if ((j0 > j1) || (j0 < 0) || (j0 >= columns) || (j1 < 0) || (j1 >= columns))
{
throw new ArgumentException("Argument out of range.");
}
MatrixV X = new MatrixV(r.Length, j1 - j0 + 1);
double[][] x = X.Array;
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
if ((r[i] < 0) || (r[i] >= this.rows))
{
throw new ArgumentException("Argument out of range.");
}
x[i][j - j0] = data[r[i]][j];
}
}
return(X);
}
/// <summary>Determines weather two instances are equal.</summary>
public static bool Equals(MatrixV left, MatrixV right)
{
if (((object)left) == ((object)right))
{
return(true);
}
if ((((object)left) == null) || (((object)right) == null))
{
return(false);
}
if ((left.Rows != right.Rows) || (left.Columns != right.Columns))
{
return(false);
}
for (int i = 0; i < left.Rows; i++)
{
for (int j = 0; j < left.Columns; j++)
{
if (left[i, j] != right[i, j])
{
return(false);
}
}
}
return(true);
}
/// <summary>Unary minus.</summary>
public static MatrixV Negate(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
int rows = value.Rows;
int columns = value.Columns;
double[][] data = value.Array;
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = -data[i][j];
}
}
return(X);
}
/// <summary>Matrix subtraction.</summary>
public static MatrixV Subtract(MatrixV left, MatrixV right)
{
if (left == null)
{
throw new ArgumentNullException("left");
}
if (right == null)
{
throw new ArgumentNullException("right");
}
int rows = left.Rows;
int columns = left.Columns;
double[][] data = left.Array;
if ((rows != right.Rows) || (columns != right.Columns))
{
throw new ArgumentException("Matrix dimension do not match.");
}
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = data[i][j] - right[i, j];
}
}
return(X);
}
/// <summary>Construct a QR decomposition.</summary>
public QrDecomposition(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
this.QR = (MatrixV)value.Clone();
double[][] qr = this.QR.Array;
int m = value.Rows;
int n = value.Columns;
this.Rdiag = new double[n];
for (int k = 0; k < n; k++)
{
// Compute 2-norm of k-th column without under/overflow.
double nrm = 0;
for (int i = k; i < m; i++)
{
nrm = Hypotenuse(nrm, qr[i][k]);
}
if (nrm != 0.0)
{
// Form k-th Householder vector.
if (qr[k][k] < 0)
{
nrm = -nrm;
}
for (int i = k; i < m; i++)
{
qr[i][k] /= nrm;
}
qr[k][k] += 1.0;
// Apply transformation to remaining columns.
for (int j = k + 1; j < n; j++)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += qr[i][k] * qr[i][j];
}
s = -s / qr[k][k];
for (int i = k; i < m; i++)
{
qr[i][j] += s * qr[i][k];
}
}
}
this.Rdiag[k] = -nrm;
}
}
/// <summary>Matrix-scalar multiplication.</summary>
public static MatrixV Multiply(MatrixV left, double right)
{
if (left == null)
{
throw new ArgumentNullException("left");
}
int rows = left.Rows;
int columns = left.Columns;
double[][] data = left.Array;
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = data[i][j] * right;
}
}
return(X);
}
/// <summary>Returns a sub matrix extracted from the current matrix.</summary>
/// <param name="i0">Starttial row index</param>
/// <param name="i1">End row index</param>
/// <param name="c">Array of row indices</param>
public MatrixV Submatrix(int i0, int i1, int[] c)
{
if ((i0 > i1) || (i0 < 0) || (i0 >= this.rows) || (i1 < 0) || (i1 >= this.rows))
{
throw new ArgumentException("Argument out of range.");
}
MatrixV X = new MatrixV(i1 - i0 + 1, c.Length);
double[][] x = X.Array;
for (int i = i0; i <= i1; i++)
{
for (int j = 0; j < c.Length; j++)
{
if ((c[j] < 0) || (c[j] >= columns))
{
throw new ArgumentException("Argument out of range.");
}
x[i - i0][j] = data[i][c[j]];
}
}
return(X);
}
public static Matrix4d Invert(Matrix4d source)
{
//Matrix4d test = ConvertDX.ToMatrix4d(Microsoft.DirectX.Matrix.Invert(ConvertDX.FromMatrix4d(source)));
MatrixV rightHandSide = MatrixV.Diagonal(4, 4, 1.0);
Matrix4d solution = new Matrix4d(new LuDecomposition(source.m_MapackMat).Solve(rightHandSide));
return(solution);
}
private Matrix4d(MatrixV mapackMat)
{
if (mapackMat.Rows != 4 || mapackMat.Columns != 4)
{
throw new ApplicationException("Only 4x4 matrices supported in Matrix4d constructor.");
}
m_MapackMat = mapackMat;
}
/// <summary>Solves a set of equation systems of type <c>A * X = B</c>.</summary>
/// <param name="value">Right hand side matrix with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>Matrix <c>X</c> so that <c>L * U * X = B</c>.</returns>
public MatrixV Solve(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows != this.LU.Rows)
{
throw new ArgumentException("Invalid matrix dimensions.", "value");
}
if (!this.NonSingular)
{
throw new InvalidOperationException("Matrix is singular");
}
// Copy right hand side with pivoting
int count = value.Columns;
MatrixV X = value.Submatrix(pivotVector, 0, count - 1);
int rows = LU.Rows;
int columns = LU.Columns;
double[][] lu = LU.Array;
// Solve L*Y = B(piv,:)
for (int k = 0; k < columns; k++)
{
for (int i = k + 1; i < columns; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * lu[i][k];
}
}
}
// Solve U*X = Y;
for (int k = columns - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= lu[k][k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * lu[i][k];
}
}
}
return(X);
}
/// <summary>Returns a diagonal matrix of the given size.</summary>
public static MatrixV Diagonal(int rows, int columns, double value)
{
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = ((i == j) ? value : 0.0);
}
}
return(X);
}
public Matrix4d(
double _M11, double _M12, double _M13, double _M14,
double _M21, double _M22, double _M23, double _M24,
double _M31, double _M32, double _M33, double _M34,
double _M41, double _M42, double _M43, double _M44
)
{
m_MapackMat = new MatrixV(new double[][] {
new double[] { _M11, _M12, _M13, _M14 },
new double[] { _M21, _M22, _M23, _M24 },
new double[] { _M31, _M32, _M33, _M34 },
new double[] { _M41, _M42, _M43, _M44 }
});
}
/// <summary>Returns a matrix filled with random values.</summary>
public static MatrixV Random(int rows, int columns)
{
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = random.NextDouble();
}
}
return(X);
}
/// <summary>Matrix-matrix multiplication.</summary>
public static MatrixV Multiply(MatrixV left, MatrixV right)
{
if (left == null)
{
throw new ArgumentNullException("left");
}
if (right == null)
{
throw new ArgumentNullException("right");
}
int rows = left.Rows;
double[][] data = left.Array;
if (right.Rows != left.columns)
{
throw new ArgumentException("Matrix dimensions are not valid.");
}
int columns = right.Columns;
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
int size = left.columns;
double[] column = new double[size];
for (int j = 0; j < columns; j++)
{
for (int k = 0; k < size; k++)
{
column[k] = right[k, j];
}
for (int i = 0; i < rows; i++)
{
double[] row = data[i];
double s = 0;
for (int k = 0; k < size; k++)
{
s += row[k] * column[k];
}
x[i][j] = s;
}
}
return(X);
}
/// <summary>Creates a copy of the matrix.</summary>
public MatrixV Clone()
{
MatrixV X = new MatrixV(rows, columns);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[i][j] = data[i][j];
}
}
return(X);
}
/// <summary>Returns the transposed matrix.</summary>
public MatrixV Transpose()
{
MatrixV X = new MatrixV(columns, rows);
double[][] x = X.Array;
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < columns; j++)
{
x[j][i] = data[i][j];
}
}
return(X);
}
/// <summary>Returns a sub matrix extracted from the current matrix.</summary>
/// <param name="startRow">Start row index</param>
/// <param name="endRow">End row index</param>
/// <param name="startColumn">Start column index</param>
/// <param name="endColumn">End column index</param>
public MatrixV Submatrix(int startRow, int endRow, int startColumn, int endColumn)
{
if ((startRow > endRow) || (startColumn > endColumn) || (startRow < 0) || (startRow >= this.rows) || (endRow < 0) || (endRow >= this.rows) || (startColumn < 0) || (startColumn >= this.columns) || (endColumn < 0) || (endColumn >= this.columns))
{
throw new ArgumentException("Argument out of range.");
}
MatrixV X = new MatrixV(endRow - startRow + 1, endColumn - startColumn + 1);
double[][] x = X.Array;
for (int i = startRow; i <= endRow; i++)
{
for (int j = startColumn; j <= endColumn; j++)
{
x[i - startRow][j - startColumn] = data[i][j];
}
}
return(X);
}
/// <summary>Returns a sub matrix extracted from the current matrix.</summary>
/// <param name="rowIndexes">Array of row indices</param>
/// <param name="columnIndexes">Array of column indices</param>
public MatrixV Submatrix(int[] rowIndexes, int[] columnIndexes)
{
MatrixV X = new MatrixV(rowIndexes.Length, columnIndexes.Length);
double[][] x = X.Array;
for (int i = 0; i < rowIndexes.Length; i++)
{
for (int j = 0; j < columnIndexes.Length; j++)
{
if ((rowIndexes[i] < 0) || (rowIndexes[i] >= rows) || (columnIndexes[j] < 0) || (columnIndexes[j] >= columns))
{
throw new ArgumentException("Argument out of range.");
}
x[i][j] = data[rowIndexes[i]][columnIndexes[j]];
}
}
return(X);
}
/// <summary>Returns the LHS solution vetor if the matrix is square or the least squares solution otherwise.</summary>
public MatrixV Solve(MatrixV rightHandSide)
{
return((rows == columns) ? new LuDecomposition(this).Solve(rightHandSide) : new QrDecomposition(this).Solve(rightHandSide));
}
/// <summary>Least squares solution of <c>A * X = B</c></summary>
/// <param name="value">Right-hand-side MatrixV with as many rows as <c>A</c> and any number of columns.</param>
/// <returns>A MatrixV that minimized the two norm of <c>Q * R * X - B</c>.</returns>
/// <exception cref="T:System.ArgumentException">MatrixV row dimensions must be the same.</exception>
/// <exception cref="T:System.InvalidOperationException">MatrixV is rank deficient.</exception>
public MatrixV Solve(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
if (value.Rows != QR.Rows)
{
throw new ArgumentException("MatrixV row dimensions must agree.");
}
if (!this.FullRank)
{
throw new InvalidOperationException("MatrixV is rank deficient.");
}
// Copy right hand side
int count = value.Columns;
MatrixV X = value.Clone();
int m = QR.Rows;
int n = QR.Columns;
double[][] qr = QR.Array;
// Compute Y = transpose(Q)*B
for (int k = 0; k < n; k++)
{
for (int j = 0; j < count; j++)
{
double s = 0.0;
for (int i = k; i < m; i++)
{
s += qr[i][k] * X[i, j];
}
s = -s / qr[k][k];
for (int i = k; i < m; i++)
{
X[i, j] += s * qr[i][k];
}
}
}
// Solve R*X = Y;
for (int k = n - 1; k >= 0; k--)
{
for (int j = 0; j < count; j++)
{
X[k, j] /= Rdiag[k];
}
for (int i = 0; i < k; i++)
{
for (int j = 0; j < count; j++)
{
X[i, j] -= X[k, j] * qr[i][k];
}
}
}
return(X.Submatrix(0, n - 1, 0, count - 1));
}
/// <summary>Construct a LU decomposition.</summary>
public LuDecomposition(MatrixV value)
{
if (value == null)
{
throw new ArgumentNullException("value");
}
this.LU = (MatrixV)value.Clone();
double[][] lu = LU.Array;
int rows = value.Rows;
int columns = value.Columns;
pivotVector = new int[rows];
for (int i = 0; i < rows; i++)
{
pivotVector[i] = i;
}
pivotSign = 1;
double[] LUrowi;
double[] LUcolj = new double[rows];
// Outer loop.
for (int j = 0; j < columns; j++)
{
// Make a copy of the j-th column to localize references.
for (int i = 0; i < rows; i++)
{
LUcolj[i] = lu[i][j];
}
// Apply previous transformations.
for (int i = 0; i < rows; i++)
{
LUrowi = lu[i];
// Most of the time is spent in the following dot product.
int kmax = Math.Min(i, j);
double s = 0.0;
for (int k = 0; k < kmax; k++)
{
s += LUrowi[k] * LUcolj[k];
}
LUrowi[j] = LUcolj[i] -= s;
}
// Find pivot and exchange if necessary.
int p = j;
for (int i = j + 1; i < rows; i++)
{
if (Math.Abs(LUcolj[i]) > Math.Abs(LUcolj[p]))
{
p = i;
}
}
if (p != j)
{
for (int k = 0; k < columns; k++)
{
double t = lu[p][k];
lu[p][k] = lu[j][k];
lu[j][k] = t;
}
int v = pivotVector[p];
pivotVector[p] = pivotVector[j];
pivotVector[j] = v;
pivotSign = -pivotSign;
}
// Compute multipliers.
if (j < rows & lu[j][j] != 0.0)
{
for (int i = j + 1; i < rows; i++)
{
lu[i][j] /= lu[j][j];
}
}
}
}